Enter inductance and capacitance, choose units, then calculate. Optional peak values estimate stored energy at voltage or current peaks.
This calculator uses the ideal LC resonance relationship:
- Angular frequency: ω0 = 1 / √(L·C)
- Resonant frequency: f0 = ω0 / (2π) = 1 / (2π√(L·C))
- Period: T0 = 1 / f0 = 2π√(L·C)
- Optional energy peaks: EC,max = ½·C·Vpk2, EL,max = ½·L·Ipk2
For real oscillators, losses and parasitics shift the frequency. Use measured L and effective C if precision matters.
- Enter the inductance value and pick its unit.
- Enter the capacitance value and pick its unit.
- Optionally add peak voltage or peak current for energy estimates.
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF after computing.
These sample combinations help validate expected ranges for tuned circuits.
| Inductance (L) | Capacitance (C) | Resonant Frequency (Approx.) | Typical Use |
|---|---|---|---|
| 10 uH | 100 pF | 5.03292 MHz | RF tank circuits |
| 1 mH | 10 nF | 50.3292 kHz | Audio filters |
| 100 uH | 1 nF | 503.292 kHz | IF stages |
| 47 mH | 1 uF | 734.127 Hz | Low-frequency oscillators |
1) What resonance means in practice
An ideal LC tank exchanges energy between an inductor and a capacitor. At resonance, the reactive effects cancel, so the tank naturally oscillates at one frequency. Designers use it for tuning, timing, and selective filtering.
2) Typical component ranges and outcomes
Inductors often span about 10 nH to 100 mH, while capacitors commonly span 1 pF to 1000 µF. Small L and C push resonance into MHz and GHz regions, while larger values pull resonance into audio or sub‑audio ranges. In many RF tanks, C is 10–470 pF and L is 50–500 nH.
3) Unit handling and scaling behavior
Because f0 depends on √(L·C), scaling is predictable. If you increase inductance by 4×, frequency drops by 2×. If you reduce capacitance by 9×, frequency rises by 3×. Unit selectors reduce power‑of‑ten mistakes.
4) Why real circuits drift from the ideal
Real inductors have winding resistance, core losses, and stray capacitance. Real capacitors have ESR, ESL, and tolerance. These parasitics shift effective L or C and reduce the quality factor Q, which broadens bandwidth and lowers peak impedance. For tighter results, use measured L and effective C at the operating frequency.
5) Quick data checks you can do
A practical tank might use L = 10 µH and C = 100 pF, giving a resonance near 159 kHz. An IF example with L = 100 µH and C = 1 nF lands near 503 kHz. If your result looks off by 10×, recheck units first.
6) Using period and angular frequency
The period T0 shows time per cycle, useful for timing and sampling. Angular frequency ω0 is preferred in equation‑based models and impedance work. Reporting f0, ω0, and T0 together speeds up design reviews.
7) Energy estimates with peak values
If you enter peak voltage, the tool estimates capacitor peak energy EC,max = ½·C·Vpk2. If you enter peak current, it estimates inductor peak energy EL,max = ½·L·Ipk2. In an ideal lossless oscillator, these peak energies should match closely.
8) Design workflow suggestions
Start with a target frequency, pick a convenient capacitor, then solve for L using L = 1/(ω02·C). Check current and voltage stress against ratings. Prototype and trim using a small variable capacitor, a tuned inductor, or a calibrated series capacitor.
It computes the ideal resonant frequency f0 from your inductance and capacitance, and also returns ω0 and the period T0 for engineering use.
The LC system is a second‑order oscillator. Its natural frequency comes from the differential equation linking inductor voltage and capacitor current, giving ω0 = 1/√(L·C).
Use the effective total capacitance seen by the inductor, including any tuning capacitor plus stray capacitance from wiring, junctions, and the inductor’s self‑capacitance when relevant.
This often happens when effective capacitance is higher than the nominal value, or when inductance shifts with core effects. Stray capacitance, ESR/ESL, and component tolerance are common causes.
The ideal resonant frequency is the same for series and parallel LC using the same L and C. Impedance behavior and bandwidth differ because loading and losses change the effective Q.
They estimate peak stored energy at the capacitor’s peak voltage and the inductor’s peak current. If both peaks are entered, the tool compares energies to highlight inconsistent assumptions.
The frequency is an ideal estimate. Accuracy depends on tolerances, temperature drift, parasitics, and circuit loading. For precision, measure L and effective C at the operating frequency.